Relative Convexity and Its Applications
Constantin P. Niculescu, Ionel Roventa
TL;DR
This paper introduces a general condition extending Jensen's inequality to non-convex domains, proves an extended majorization theorem, and offers new insights into risk aversion in finance.
Contribution
It presents a novel condition for Jensen's inequality applicability, extends the Hardy-Littlewood-Pólya majorization theorem, and explores implications for risk aversion in finance.
Findings
Extended Jensen's inequality for non-convex domains
Generalized Hardy-Littlewood-Pólya majorization theorem
New insights into risk aversion in mathematical finance
Abstract
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the Hardy-Littlewood-P\'olya theorem of majorization is proved and new insight is given into the problem of risk aversion in mathematical finance.
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Taxonomy
TopicsRisk and Portfolio Optimization · Mathematical Inequalities and Applications